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Thursday, May 2, 2013

Harden Versus Elite Defenses

One of the stories right now is the supposed implosion of James Harden, the breakthrough shooting guard who's lauded for his scoring efficiency but receives heavy backlash from people who hate his flopping and deride his game, calling it bland and, since he has no midrage game, devoid of skill. Critics also imply he's somehow paying off the refs or the league has an interest in his success, like it would make sense to conspire in an effort that could get you fired for propping up the NBA markets of Oklahoma City and Houston. Now there's a widespread declaration that he shrinks in playoff games and against good defenses, coming of a disappointing finals from the 2012 season and the recency bias of some high turnover games against the Thunder. While the playoff woes deserve a little more time because you can't judge a player based on so few games, Harden just spent an entire season as the number one scoring offense and we should be able to tell if he indeed struggles against top defenses.

Methods to the madness
There actually isn't a single straightforward way to judge how well someone fared against a defense. Points doesn't tell you how many shots someone missed or turnovers created. Focusing on shooting efficiency doesn't account for more of an offensive burden: if you take more shots, your efficiency typically decreases. There are lots of single number metrics (too many, honestly), but not all have an only offense component and none are perfect. The best approach is to analyze this from multiple angles and look for patters, as well as comparing Harden's output to that from the league's other top scorers.

But what myths are we looking to bust? Does Harden perform worse as the defense gets better? Generally, every player gets worse as the defense gets better, because it's better defense. I'll separate all the different hypotheses about the general myth of Harden shrinking versus top clubs.

2) Hypothesis: Harden's offense performs worse than expected as opposing defenses get better. Expectation is based on the opposing team's allowed points per possessions.

3) Hypothesis: Harden's offense performs worse compared to other high scorers as opposing defenses get better.

The data
Using basketball-reference's team defensive ratings and their offensive efficiency rating for players, I've produced the graph below. Usage percentage is the percentage of team possessions a player uses based on field goals, free throws, and turnovers. I've coded usage with color so you can see if Harden is getting less attempts in games against elite defenses, and everything is on a per possession basis so there's no bias in pace or minutes played.

I don't see how there's any pattern between Harden's scoring and the opposing team's defensive rating, and unless you're John Nash you won't find one either. People may get distracted by the clump of low efficiency games versus the league's two best defenses, Memphis and Indiana, but he had another game versus Memphis with an offensive rating of 153 and above average usage -- and yes, Tony Allen and Marc Gasol played, and Memphis was blown out. Additionally, he had a string of good games versus the league's third best offense the Spurs. Using regression, you can test whether or not the defense is a significant predictor of various offensive stats. I've included a summary below, and the results are much like the scatterplot: there is no link. I've also used home/away games as a dummy variable, in case that was influencing the result. It's an interesting sidenote, but with Harden and the other top scorers their production does not appear to be significantly affected by away games.

Offensive rating

Offensive game
score

Points/minute

Usage %

Assist %

Coefficient

0.885

0.319

0.216

0.118

0.409

p-value

35%

28%

36%

50%

33%

*Offensive game score is the game score outlined here but without the defensive components

The most telling fact from the results is that none are statistically significant (near the 5% p-value threshold.) There's simply too much noise and variation. He doesn't appear to perform worse in a systemic way. The offensive rating coefficient is interesting. Since it's on the same scale as the defense (the dependent variable), a coefficient less than one means Harden is performing better than expected. (This can also be taken as an inelastic value.) The best way to understand the coefficients is to think of the league's best defense with a rating around 100 and one of the league's worst defenses with a rating around 110. With a ten unit decrease (going from a terrible defense to an elite one), Harden's points per 36 minutes only decreases by two points, his assist percentage by 4%, his offensive rating by 9, etc.

How does he compare versus the other top scorers? Using the same basic regression of offensive rating or usage % versus the opposing team's defensive rating (points allowed per 100 possessions), I created two tables for easy comparisons. Keep in mind the scale and units of the coefficients, and that negative means you're actually improving as the defenses get better. The p-value shows statistical significance (anything around 5% or lower.)

The results are surprising. In offensive rating, Harden performs better than anyone except for Carmelo Anthony. Harden maintains a healthy offensive rating as the defenses get better, and his usage is only slightly decreased. Keep in mind that his results aren't statistically significant, so you can't actually say he performs better or worse. However, the other scorers are more interesting. Durant's efficiency plummets (a coefficient of 2.8 is huge), while he increases his scoring load a far amount, but not enough to offset his efficiency. Both Kobe and James see their efficiency take a dive, and they don't see a significant ride in usage to counteract it.

Offensive rating versus opposing defensive rating

James Harden

Carmelo Anthony

Kevin Durant

Kobe Bryant

LeBron James

Coefficient

0.885

0.282

2.82

1.74

2.18

p-value

35%

77%

0.029%

3.1%

0.31%

Usage rating versus opposing defensive rating

James Harden

Carmelo Anthony

Kevin Durant

Kobe Bryant

LeBron James

Coefficient

0.118

-0.0731

-0.431

-0.176

-0.108

p-value

50%

77%

4.5%

47%

51%

Of course, team roles play an important part because elite defenses are better at certain techniques of flooding the strong side of the court or controlling the top scorer with a premier wing defender. But Harden has a tougher role than some of the other stars: he's the only focal point on offense and the only top creator. James has Wade, Durant had Westbrook, and at least Kobe had Howard, who demanded more defensive attention than anyone else on Houston's team.

Speaking of team effects, one might wonder if Houston performs worse against better defensive teams in the regular season. Well, this is pretty easy to test. Using b-ref's definition of offensive/defensive efficiency, I grabbed Houston's data from the regular season and calculated their offensive efficiency in each game to compare it to the defensive efficiency of their opponent, and used regression (again.) Basically, Houston has a coefficient of 1.08 for defense, which means they play slightly worse than expected versus better defenses, but it's so slight it may not be significant. So I then constructed an expected efficiency differential. This is just the difference between Houston's offensive efficiency for a game and the opposing team's defensive rating for the season, along with the effect of homecourt advantage. Just to be sure, I did this with an assumed homecourt advantage for Houston of 2.32 and league average of 3.23 from this study, and again with home and away as dummy variables so the model calculated its own homecourt advantage numbers.

Long story short, Houston's offense does not perform significantly worse than average. For the expected efficiency differential model with HCA built in, the coefficient for defensive efficiency was only 0.0108 -- translated, in going from an elite defense (rating of 100) to a crappy one (rating of 110) they'd be only 0.108 points per 100 possessions worse than expected. The variable wasn't significant -- or close to it. (As a fun statistical side note, the standard error was forty-six (!!) times larger than the coefficient, and the R^2 value was a minuscule 5.8*10^-5.)

Hypothesis 1: Does Harden's offense get worse as defenses get better?
There appears to be a slight relationship of team defense and his offense, but it's not statistically significant. Hypothesis 1 is actually rejected.

Hypothesis 2: Does Harden's offense perform worse than expected as defenses get better?
Since hypothesis 1 was rejected, this one also falls, and actually Harden was performing better than expected (due to his coefficient being less than one for offensive efficiency) by some metrics.

Hypothesis 3: Does Harden's offense perform worse compared to other top scorers as the defenses get better?
No, and actually he looks better in comparison. This one, however, will be the focus of future research (how top scorers fare against top defenses.)

Harden may depend on his foul drawing abilities for his scoring, but this is true of many elite wing scorers in the past from Jerry West to Jordan. Perhaps he's a playoff underperformer, but he hasn't played enough yet to brand him with such a slanderous accusation. Being called a playoff failure is a career killer, as David Robinson knows all too well. He doesn't have a midrange game, but he's one of the few players who can successfully shoot three-pointers at a healthy percentage off his dribble, and his team doesn't perform worse than expected as defenses get better. Being dependent on the two most valuable shots (three-pointers and at the rim attempts) in the game should in fact be considered a strength. The Beard has his detractors, but his game is holding up.

Edited: Added a section on how Houston performs as defenses get better.